SOLUTION: h(x) = ln(x + 9) To sketch the graph of the function, first rewrite the logarithmic equation in the exponential form. ? = x + 9 Solve for x. x = ?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: h(x) = ln(x + 9) To sketch the graph of the function, first rewrite the logarithmic equation in the exponential form. ? = x + 9 Solve for x. x = ?       Log On


   

Question 890517: h(x) = ln(x + 9)
To sketch the graph of the function, first rewrite the logarithmic equation in the exponential form.

? = x + 9
Solve for x.
x = ?
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Same gragh as for ln(x) but shifted to the left by 9 units.

graph%28300%2C300%2C-10%2C5%2C-10%2C10%2Cln%28x%2B9%29%29
The curve is supposed to be shown continuing to extend downward on the left.

h%28x%29+=+ln%28x+%2B+9%29

e%5E%28h%28x%29%29=x%2B9 exponential form.

x=e%5E%28h%28x%29%29-9 shows x in terms of h(x).

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!

the log equation is equivalent to the exponential equation as defined by the identity equation shown below:

logb(a) = y if and only if b^y = a

this statement reads:

log of a to the base of b is equal to y if and only if the base of b raised to the power of y is equal to a.

this works for any base, including the base of e which is what LN represents.

ln(x + 9) = loge(x + 9)

e is the scientific constant of 2.718281828...

this statement says that the natural log of (x + 9) is equal to the log of (x + 9) to the base of e.

your equation of ln(x + 9) is equivalent to loge(x + 9).

the log identity formula applied to your problem is:

loge(x+9) = y if and only if e^y = x + 9

if you solve for x in this equation, you get x = e^y - 9

instead of x being the independent variable, y is the independent variable.

the graph of y = ln(x+9) is identical to the graph of x = e^y - 9.

i'll show you that further down.

normally you choose values for x and find the equivalent value of y through the use of the formula.

here you will choose values for y and find the equivalent value of x through the use of the formula.

then you graph the coordinate points that you have.

create a table with values for y from y = -4 to + 4 and calculate x = e^y - 9 for each value of y.

your table will look like this: 


y     x

-4    -8.98
-3    -8.95
-2    -8.87
-1    -8.63
 0    -8.00
 1    -6.28
 2    -1.61
 3     11.09
 4     45.60


you are looking for the value of y and then finding the corresponding value of x.

the graph of your equation of x = e^y - 9 will look like this:

$$$

this is identical to the grah of y = ln(x+9) that is shown below:

$$$